In a conventional cone beam X-ray computerized tomography (CB CT) system a source of radiation is placed opposite an array of detectors which are arranged in a manner such that the position of the detector array is fixed relative to the source. The source and detectors are then moved mechanically relative to an object being imaged. In some systems, the object is kept stationary and the source-detector assembly is moved, whereas in others the source and detectors are rotated around the object while the object is translated. Some systems are configured such that the source describes a helical trajectory relative to the object. The rate at which tomographic images can be acquired by such systems is limited by the rate of rotation of the assembly supporting the source and detector array.
In X-ray tomography systems such as in a Real Time Tomography (RTT) system for example, a plurality of X-ray sources are arranged around a circle, however more general arrangements of sources along curves encircling the region of interest are possible. These sources are switched on and off in a sequence in order to obtain the same effect as obtained from a single rotating radiation source. In such systems, a detector cannot be placed opposite a given source as that position is occupied by another source. This renders attenuation along rays that make less than a particular limiting angle to the plane of the sources immeasurable. Such systems maybe termed as “offset detector” systems.
In contrast to the conventional and standard helical cone beam tomography system, for such an “offset detector” system no plane exists in which attenuation along all rays are measured. Hence, a simple two dimensional inverse Radon transform cannot be used to reconstruct an image on that plane. One known method for regaining efficiency of two dimensional reconstructions for such a system is to approximate the line integrals along rays in a plane using integrals along rays that lie close to that plane. A more general method called surface rebinning is to approximate using lines close to a surface.
For a given detector array shape and size and source trajectory, it is possible to calculate an optimal rebinning surface using the fixed point algorithm known in the art. This method can also be used, with some modification, when the extent of the detector is limited, as is in offset systems, or more generally, systems where the detector is not symmetrical in an axial direction with respect to the active source. However in the case of an offset detector approximation with rays close to one surface can result in poor image reconstruction due to absence of rays making an acute angle to the source plane.
Hence, there is need for a method of reconstructing images from a tomographic system in which detectors are not located directly opposite radiation sources.